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# If the absolute temperature of a sample in a fixed volume container is quadrupled then the root mean square speed in the initial state $u_i$ and that in the final stage $u_f$ would be related as:

$(a)\;u_f=\large\frac{u_i}{4}\qquad(b)\;u_f=\large\frac{u_i}{2}\qquad(c)\;u_f=2u_i\qquad(d)\;u_f=4u_i$

$u_i \propto \sqrt{T_1}$
$u_f \propto \sqrt{T_2}$
(Since $u = \sqrt{\large\frac{3RT}{m}})$
$T_2 = 4T_1$
$\large\frac{u_i}{u_f} = \sqrt{\large\frac{T_1}{T_2}}$
$=\sqrt{\large\frac{T_1}{4T_1}} = \large\frac{1}{2}$
$\Rightarrow u_f = 2u_i$